In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts. Alternatively, mathematics can be taught through problem solving as the teacher poses carefully selected problems that enable students to develop their understanding of new concepts and skills. In this article, the authors expand on those approaches by considering problem solving as the act of doing mathematics. The authors recommend introducing unsolved problems as a means of challenging students' current perceptions of mathematics (doing math) by having them engage in some of the accessible aspects of the work of mathematicians.